Question 1

Solve Systems of Linear Equations in Three Variables
-$$\begin{array} { l } 
2 x + 2 y + z = - 10 \
4 x - 2 y - z = - 20 \
2 x + y + 2 z = - 13
\end{array}$$

Accepted Answer

A)  $\{ ( - 5,1 , - 2 ) \}$ 
B)  $\{ ( - 5 , - 2,1 ) \}$ 
C)  $\{ ( - 2,1 , - 5 ) \}$ 
D)  $\{ ( 1 , - 5 , - 2 ) \}$ 
A)  $\{ ( - 5,1 , - 2 ) \}$ 
B)  $\{ ( - 5 , - 2,1 ) \}$ 
C)  $\{ ( - 2,1 , - 5 ) \}$ 
D)  $\{ ( 1 , - 5 , - 2 ) \}$

Question 2

Solve Problems Using Systems of Linear Equations
-In Miguel's home town, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. The function $y = 0.27 x + 14.2$ models the percentage, $y$, of women in this city who smoke x years after 1990 . The function $0.20 \mathrm { x } + \mathrm { y } = 29.7$ models the percentage, $\mathrm { y }$, of men in this city who smoke x years after 1990 . Use these models to determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time?

Accepted Answer

A)  $2023 ; 23 \%$ 
B)  $2024 ; 23 \%$ 
C)  $2022 ; 23 \%$ 
D)  $2025 ; 23 \%$ 
A)  $2023 ; 23 \%$ 
B)  $2024 ; 23 \%$ 
C)  $2022 ; 23 \%$ 
D)  $2025 ; 23 \%$

Question 3

Graph the inequality.
-$y+6<x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

Use Linear Programming to Solve Problems
-A candy company has 125 pounds of cashews and 150 pounds of peanuts which they combine into two different mixes. The deluxe mix has half cashews and half peanuts and sells for $\$ 6$ per pound. The economy mix has one third cashews and two thirds peanuts and sells for $\$ 4.60$ per pound. How many pounds of each mix should be prepared for maximum revenue?

Accepted Answer

A)  200 pounds of deluxe and 75 pounds of economy 
B)  300 pounds of deluxe and 50 pounds of economy 
C)  100 pounds of deluxe and 25 pounds of economy 
D)  125 pounds of deluxe and 0 pounds of economy 
A)  200 pounds of deluxe and 75 pounds of economy 
B)  300 pounds of deluxe and 50 pounds of economy 
C)  100 pounds of deluxe and 25 pounds of economy 
D)  125 pounds of deluxe and 0 pounds of economy

Question 5

Linear Programming
1 Write an Objective Function Describing a Quantity That Must be Maximized or Minimized
-A steel company produces two types of machine dies, part A and part B. The company makes a $\$ 2.00$ profit on each part A that it produces and a $\$ 6.00$ profit on each part $B$ that it produces. Let $x =$ the number of part A produced in a week and $\mathrm { y } =$ the number of part B produced in a week. Write the objective function that describes the total weekly profit.

Accepted Answer

A)  $z = 2 x + 6 y$ 
B)  $z = 6 x + 2 y$ 
C)  $z = 8 ( x + y )$ 
D)  $z = 2 ( x - 6 ) + 6 ( y - 2 )$ 
A)  $z = 2 x + 6 y$ 
B)  $z = 6 x + 2 y$ 
C)  $z = 8 ( x + y )$ 
D)  $z = 2 ( x - 6 ) + 6 ( y - 2 )$

Question 6

Write the partial fraction decomposition of the rational expression.
-$$\frac { 14 x ^ { 2 } - 48 x - 54 } { x ( x - 6 ) ( x + 3 ) }$$

Accepted Answer

A)  $\frac { 3 } { x } + \frac { 3 } { x - 6 } + \frac { 8 } { x + 3 }$ 
B)  $\frac { 3 } { x } + \frac { 4 } { x - 6 } + \frac { 7 } { x + 3 }$ 
C)  $\frac { 3 } { x } + \frac { 2 } { x - 6 } + \frac { 9 } { x + 3 }$ 
D)  $\frac { x + 3 } { x ^ { 2 } - 6 } + \frac { 8 } { x + 3 }$ 
A)  $\frac { 3 } { x } + \frac { 3 } { x - 6 } + \frac { 8 } { x + 3 }$ 
B)  $\frac { 3 } { x } + \frac { 4 } { x - 6 } + \frac { 7 } { x + 3 }$ 
C)  $\frac { 3 } { x } + \frac { 2 } { x - 6 } + \frac { 9 } { x + 3 }$ 
D)  $\frac { x + 3 } { x ^ { 2 } - 6 } + \frac { 8 } { x + 3 }$

Question 7

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
-$$\begin{array} { l } 
x - 3 y = 5 \
- 6 x - 4 y = 36
\end{array}$$

Accepted Answer

A)  $\{ ( - 4 , - 3 ) \}$ 
B)  $\{ ( - 5 , - 2 ) \}$ 
C)  $\{ ( x , y ) \mid x - 3 y = 5 \}$ 
D)  $\varnothing$ 
A)  $\{ ( - 4 , - 3 ) \}$ 
B)  $\{ ( - 5 , - 2 ) \}$ 
C)  $\{ ( x , y ) \mid x - 3 y = 5 \}$ 
D)  $\varnothing$

Question 8

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Solve Problems Using Systems of Linear Equations
-At the break-even point both cost and revenue are what?

Accepted Answer

A)  $\$ 2250$ 
B)  $\$ 750$ 
C)  $\$ 1500$ 
D)  $\$ 2700$ 
A)  $\$ 2250$ 
B)  $\$ 750$ 
C)  $\$ 1500$ 
D)  $\$ 2700$

Question 10

Solve Nonlinear Systems By Substitution
-$$\begin{array} { l } 
4 x - y = 1 \
y = x ^ { 2 } - 6
\end{array}$$

Accepted Answer

A)  $\{ ( - 1 , - 5 ) , ( 5,19 ) \}$ 
B)  $\{ ( 1 , - 5 ) , ( - 5,19 ) \}$ 
C)  $\{ ( - 1,7 ) , ( 5,31 ) \}$ 
D)  $\{ ( 1 , - 5 ) , ( 5,19 ) \}$ 
A)  $\{ ( - 1 , - 5 ) , ( 5,19 ) \}$ 
B)  $\{ ( 1 , - 5 ) , ( - 5,19 ) \}$ 
C)  $\{ ( - 1,7 ) , ( 5,31 ) \}$ 
D)  $\{ ( 1 , - 5 ) , ( 5,19 ) \}$

Question 11

Graph the inequality.
-$$x + 4 y \geq 1$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Partial Fractions
1 Decompose P/Q, Where Q Has Only Distinct Linear Factors
-$$\frac { 6 x + 5 } { x ^ { 2 } - 12 x + 35 }$$

Accepted Answer

A)  $\frac { A } { x - 5 } + \frac { B } { x - 7 }$ 
B)  $\frac { \mathrm { A } } { \mathrm { x } - 5 } + \frac { \mathrm { B } } { \mathrm { x } - 7 } + \frac { \mathrm { C } } { \mathrm { x } ^ { 2 } - 12 \mathrm { x } + 35 }$ 
C)  $\frac { A } { x - 5 } + \frac { B } { x - 7 } + \frac { C x + D } { x ^ { 2 } - 12 x + 35 }$ 
D)  $\frac { A } { x - 5 } + \frac { B } { x - 7 } + \frac { C } { ( x - 5 ) ^ { 2 } ( x - 7 ) ^ { 2 } }$ 
A)  $\frac { A } { x - 5 } + \frac { B } { x - 7 }$ 
B)  $\frac { \mathrm { A } } { \mathrm { x } - 5 } + \frac { \mathrm { B } } { \mathrm { x } - 7 } + \frac { \mathrm { C } } { \mathrm { x } ^ { 2 } - 12 \mathrm { x } + 35 }$ 
C)  $\frac { A } { x - 5 } + \frac { B } { x - 7 } + \frac { C x + D } { x ^ { 2 } - 12 x + 35 }$ 
D)  $\frac { A } { x - 5 } + \frac { B } { x - 7 } + \frac { C } { ( x - 5 ) ^ { 2 } ( x - 7 ) ^ { 2 } }$

Question 13

Systems of Linear Equations in Three Variables
1 Verify the Solution of a System of Linear Equations in Three Variables
-$$\begin{array} { l } 
( 3,1,5 ) \
5 x + 4 y + z = 32 \
3 x - 3 y - z = 9 \
5 x + y + 4 z = 38
\end{array}$$

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 14

Systems of Nonlinear Equations in Two Variables
1 Recognize Systems of Nonlinear Equations in Two Variables
-$$\left\{ \begin{array} { l } 
y = x ^ { 2 } - 2 \
x ^ { 2 } + y ^ { 2 } = 7
\end{array} \right.$$

Accepted Answer

A)  Nonlinear 
B)  Linear 
A)  Nonlinear 
B)  Linear

Question 15

Write the partial fraction decomposition of the rational expression.
-$\frac { 12 x - 52 } { ( x - 1 ) ( x - 6 ) }$

Accepted Answer

A)  $\frac { 8 } { x - 1 } + \frac { 4 } { x - 6 }$ 
B)  $\frac { 11 } { x - 1 } + \frac { 1 } { x - 6 }$ 
C)  $\frac { 7 } { x - 1 } + \frac { 5 } { x - 6 }$ 
D)  $\frac { 8 } { x - 1 } + \frac { - 4 } { x - 6 }$ 
A)  $\frac { 8 } { x - 1 } + \frac { 4 } { x - 6 }$ 
B)  $\frac { 11 } { x - 1 } + \frac { 1 } { x - 6 }$ 
C)  $\frac { 7 } { x - 1 } + \frac { 5 } { x - 6 }$ 
D)  $\frac { 8 } { x - 1 } + \frac { - 4 } { x - 6 }$

Question 16

Solve Problems Using Systems of Nonlinear Equations
-Find the dimensions of a rectangle whose perimeter is 44 feet and whose area is 117 square feet.

Accepted Answer

A)  9 feet by 13 feet 
B)  8 feet by 14 feet 
C)  10 feet by 12 feet 
D)  8 feet by 12 feet 
A)  9 feet by 13 feet 
B)  8 feet by 14 feet 
C)  10 feet by 12 feet 
D)  8 feet by 12 feet

Question 17

Solve Problems Using Systems of Linear Equations
-A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width.

Accepted Answer

A)  12 inches 
B)  23 inches 
C)  34 inches 
D)  35 inches 
A)  12 inches 
B)  23 inches 
C)  34 inches 
D)  35 inches

Question 18

Solve Linear Systems by Addition
-$$\begin{array} { l } 
x + y = - 8 \
x - y = 19
\end{array}$$

Accepted Answer

A)  $\{ ( 5.5 , - 13.5 ) \}$ 
B)  $\{ ( 5.5,13.5 ) \}$ 
C)  $\{ ( 8 , - 13.5 ) \}$ 
D)  $\{ ( 8,5.5 ) \}$ 
A)  $\{ ( 5.5 , - 13.5 ) \}$ 
B)  $\{ ( 5.5,13.5 ) \}$ 
C)  $\{ ( 8 , - 13.5 ) \}$ 
D)  $\{ ( 8,5.5 ) \}$

Question 19

Solve Problems Using Systems in Three Variables
-The following is known about three numbers: If the second number is subtracted from the sum of the first number and 3 times the third number, the result is $- 7$. The third number plus 2 times the first number is $- 2$. The first number plus 5 times the second number plus the third number is 3 . Find the three numbers. [Hint: let $x$ represent the first number, $y$ the second number, and $z$ the third number. Use the given conditions to write and solve a system of equations.]

Accepted Answer

A)  $x = 0 , y = 1 , z = - 2$ 
B)  $x = 1 , y = 2 , z = - 2$ 
C)  $x = - 1 , y = 1 , z = 0$ 
D)  $x = 0 , y = 0 , z = 3$ 
A)  $x = 0 , y = 1 , z = - 2$ 
B)  $x = 1 , y = 2 , z = - 2$ 
C)  $x = - 1 , y = 1 , z = 0$ 
D)  $x = 0 , y = 0 , z = 3$

Question 20

Solve Problems Using Systems of Linear Equations
-Julie and Eric row their boat (at a constant speed) 27 miles downstream for 3 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current.

Accepted Answer

A)  $3 \mathrm { mph }$ 
B)  $6 \mathrm { mph }$ 
C)  $4 \mathrm { mph }$ 
D)  $2.5 \mathrm { mph }$ 
A)  $3 \mathrm { mph }$ 
B)  $6 \mathrm { mph }$ 
C)  $4 \mathrm { mph }$ 
D)  $2.5 \mathrm { mph }$

Solve Systems of Linear Equations in Three Variables - 2x+2y+z=-10 4x-2y-z=-20 2x+y+2z=-13

Graph the inequality. - $y+6<x$

Write the partial fraction decomposition of the rational expression. - $\frac { 14 x ^ { 2 } - 48 x - 54 } { x ( x - 6 ) ( x + 3 ) }$

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - x-3y=5 -6x-4y=36

Graph the solution set of the system of inequalities or indicate that the system has no solution. -

Solve Problems Using Systems of Linear Equations -At the break-even point both cost and revenue are what?

Solve Nonlinear Systems By Substitution - 4x-y=1 y=-6

Graph the inequality. - $x + 4 y \geq 1$ $Graph the inequality. - x + 4 y \geq 1$

Partial Fractions 1 Decompose P/Q, Where Q Has Only Distinct Linear Factors - $\frac { 6 x + 5 } { x ^ { 2 } - 12 x + 35 }$

Systems of Linear Equations in Three Variables 1 Verify the Solution of a System of Linear Equations in Three Variables - (3,1,5) 5x+4y+z=32 3x-3y-z=9 5x+y+4z=38

Systems of Nonlinear Equations in Two Variables 1 Recognize Systems of Nonlinear Equations in Two Variables - $\left\{ \begin{array} { l } y = x ^ { 2 } - 2 \\x ^ { 2 } + y ^ { 2 } = 7\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x - 52 } { ( x - 1 ) ( x - 6 ) }$

Solve Problems Using Systems of Nonlinear Equations -Find the dimensions of a rectangle whose perimeter is 44 feet and whose area is 117 square feet.

Solve Problems Using Systems of Linear Equations -A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width.

Solve Linear Systems by Addition - x+y=-8 x-y=19

Solve Problems Using Systems of Linear Equations -Julie and Eric row their boat (at a constant speed) 27 miles downstream for 3 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 8: Systems of Equations and Inequalities

Solve Systems of Linear Equations in Three Variables - 2x+2y+z=-10 4x-2y-z=-20 2x+y+2z=-13

Graph the inequality. - y+6&lt;x

Write the partial fraction decomposition of the rational expression. - 14x2−48x−54x(x−6)(x+3)\frac { 14 x ^ { 2 } - 48 x - 54 } { x ( x - 6 ) ( x + 3 ) }x(x−6)(x+3)14x2−48x−54​

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - x-3y=5 -6x-4y=36

Graph the solution set of the system of inequalities or indicate that the system has no solution. -

Solve Problems Using Systems of Linear Equations -At the break-even point both cost and revenue are what?

Solve Nonlinear Systems By Substitution - 4x-y=1 y=-6

Graph the inequality. - x+4y≥1x + 4 y \geq 1x+4y≥1

Partial Fractions 1 Decompose P/Q, Where Q Has Only Distinct Linear Factors - 6x+5x2−12x+35\frac { 6 x + 5 } { x ^ { 2 } - 12 x + 35 }x2−12x+356x+5​

Systems of Linear Equations in Three Variables 1 Verify the Solution of a System of Linear Equations in Three Variables - (3,1,5) 5x+4y+z=32 3x-3y-z=9 5x+y+4z=38

Systems of Nonlinear Equations in Two Variables 1 Recognize Systems of Nonlinear Equations in Two Variables - {y=x2−2x2+y2=7\left\{ \begin{array} { l } y = x ^ { 2 } - 2 \\x ^ { 2 } + y ^ { 2 } = 7\end{array} \right.{y=x2−2x2+y2=7​

Write the partial fraction decomposition of the rational expression. - 12x−52(x−1)(x−6)\frac { 12 x - 52 } { ( x - 1 ) ( x - 6 ) }(x−1)(x−6)12x−52​

Solve Problems Using Systems of Nonlinear Equations -Find the dimensions of a rectangle whose perimeter is 44 feet and whose area is 117 square feet.

Solve Problems Using Systems of Linear Equations -A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width.

Solve Linear Systems by Addition - x+y=-8 x-y=19

Solve Problems Using Systems of Linear Equations -Julie and Eric row their boat (at a constant speed) 27 miles downstream for 3 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Graph the inequality. - $y+6<x$

Write the partial fraction decomposition of the rational expression. - $\frac { 14 x ^ { 2 } - 48 x - 54 } { x ( x - 6 ) ( x + 3 ) }$

Graph the inequality. - $x + 4 y \geq 1$ $Graph the inequality. - x + 4 y \geq 1$

Partial Fractions 1 Decompose P/Q, Where Q Has Only Distinct Linear Factors - $\frac { 6 x + 5 } { x ^ { 2 } - 12 x + 35 }$

Systems of Nonlinear Equations in Two Variables 1 Recognize Systems of Nonlinear Equations in Two Variables - $\left\{ \begin{array} { l } y = x ^ { 2 } - 2 \\x ^ { 2 } + y ^ { 2 } = 7\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x - 52 } { ( x - 1 ) ( x - 6 ) }$